Numerous physical structures of commercial interest, including optical fibers, semiconductor lasers, quantum well infrared photo-detectors and the like have physical behavior governed by the solution of a wave equation in a medium consisting of multiple materials. Solution to this equation may be essential in the design process of such structures.
Traditionally, mathematical techniques, such as finite difference methods or shooting methods such as the transfer matrix and transmission line analogy, are used to compute eigenvalues and eigenfunctions in such structures and systems. While such techniques provide accurate solutions, these techniques are usually mathematically inefficient, requiring large matrices and significant computation time. Furthermore, it is difficult to apply the above-mentioned techniques to open system wave problems, without additional steps of domain truncation and imposing transparent boundary conditions.